LONDON—Hours after the third terrorist attack in the U.K. in three months, British leaders escalated their criticism of Silicon Valley, calling for international regulations to hinder extremists who use cyberspace to spread their message and recruit supporters.

“We cannot allow this ideology the safe space it needs to breed,” British Prime Minister Theresa May said on Sunday, the morning after a London attack killed at least seven people and injured scores more. “Yet that is precisely what the internet and the big companies...